Random projections of regular polytopes
- Cite this article as:
- Böröczky, Jr., K. & Henk, M. Arch. Math. (1999) 73: 465. doi:10.1007/s000130050424
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Based on an approach of Affentranger & Schneider we give an asymptotic formula for the expected number of k-faces of the orthogonal projection of a regular n-crosspolytope onto a randomly chosen isotropic subspace of fixed dimension, as n tends to infinity. In particular, we present a precise asymptotic formula for the (spherical) volume of spherical regular simplices, which generalizes Daniel's formula.